
Example
For a given function f(x, y) = xy on unit disk Ω ⊂ R
2
, nd a function u(x, y) satisfying :
−∆u(x, y) = f(x, y) in Ω
u(x, y) = 0 on ∂Ω
(1)
The boundary C = ∂Ω is denoted by:
C = {(x, y)|x = cos(t), y = sin(t), 0 ≤ t < 2π}
Weak Formulation of Equation(1)
Find u ∈ H
1
0
(Ω) s.t
∫
Ω
∇u · ∇v dxdy =
∫
Ω
fv dxdy ∀v ∈ H
1
0
(Ω) (2)
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